The midfielder endured a torrid night in Armenia as the SPFL Premiership side lost 1-0 in their first qualifying round tie against Alashkert.
After needing treatment to a head wound for six minutes having collided with his own goalkeeper Alan Mannus 30 seconds into the game, Davidson was hurt again before half time.
This time the long-term effects were thought to be more significant and the 27-year-old could face a lengthy spells on the sidelines.
Davidson has had a series of knee problems and missed eight months last year after rupturing a tendon. He now faces an anxious wait to see the extent of his latest problem.
Manager Tommy Wright said: “It is a major concern. Initial reports suggest it could be his cruciate ligament, so that is not good.
“He is distraught and I am looking at losing him for most of the season. It doesn’t take away the disappointment of our defeat – but it puts it into perspective.
“He’s someone who has gone through the mill with injuries. Hopefully the early reports are wrong but it doesn’t look great.”
Wright’s team were beaten by a strike from substitute Mihran Manasyan just before the hour mark but he is still hopeful of turning things around in the return fixture at McDiarmid Park.
“It almost took the goal for us to react and to kick into gear and that’s disappointing,” he added.
“Once we went behind, I think we were the slightly better side. We moved a lot quicker and created a few opportunities.
“We couldn’t get that goal, which would have been a really good result away from home, but we are only 1-0 down and the tie is very much alive.”